Question

14.4.22 A Question Help 0 Consider the set of ordered pairs shown below. Assuming that the regression equation is y = 5.413-0.239x and the SSE = 10.674, construct a 95% confidence interval for x = 2 2 X у 2 5 3 5 14 6 6 Click the icon to view a portion of the student's t-distribution table. မဟ Calculate the upper and lower limits of the confidence interval. UCL = LCL = (Round to three decimal places as needed.)

Answer 1

Sxx =Σ (Xi - X̅ )2 =    9.2
Syy = Σ( Yi - Y̅ )2 =    11.2
Sxy = Σ (Xi - X̅ ) * (Yi - Y̅) =    8.36

X̅ = Σ( Xi / n ) = 17/5 = 3.4
Y̅ = Σ( Yi / n ) = 23/5 = 4.6

Standard Error of Estimate S = √ ( Σ (Y - Ŷ ) / n - 2) = √(10.6739 / 3) = 1.886

Confidence Interval of    $\mu_{Y|X = 2}$
Ŷ = 5.413 + -0.2391 X
Ŷ = 4.935

t(α/2) = t(0.05/2) =3.182

se[160] ta/2 (.30 – 7)? + -] x 92 n Sri

95% confidence interval is ( 1.077 < $\mu_{Y|X = 2}$ < 8.793 )